期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 25, 期 13, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127415300384
关键词
High-order-quasi-zero-stiffness; high-static-low-dynamic-stiffness; SD oscillator; multiple stability; bifurcation; chaos
资金
- National Natural Science Foundation of China [11372082, 11572096]
- National Basic Research Program of China [2015CB057405]
A novel nonlinear oscillator with multiple stabilities is proposed in this paper based on the original SD oscillator [Cao et al., 2006] and the generalized SD oscillator [Han et al., 2012; Cao et al., 2014]. The mathematical model of this system is formulated by using Lagrange equation. Even when all the springs are linear, the system admits strongly irrational nonlinearities due to the geometry configuration. The investigation shows that the nonlinear oscillator exhibits complex equilibrium bifurcations of single-, double-, triple- and quadruple-well properties, and the singular closed orbits of homoclinic, heteroclinic and homo-heteroclinic types as well for both smooth and discontinuous cases. The chaotic behaviors are also presented numerically for the perturbed system under the perturbation of both viscous-damping and external excitation. This oscillator can be extended to a high-order-quasi-zero-stiffness isolator and a nonlinear supporting system for ground vibration test for large-scale structures to achieve the high-staticlow-dynamic-stiffness.
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